Since Sunday, the community has been working to accommodate hundreds of people already released at a bus station, officials said.

At least 180 "migrants were dropped off today [Christmas Day] in downtown El Paso staggered through the afternoon, starting at 1:30pm local time," Dylan Corbett, the director of Hope Border Institute, told CNN.

"About half of them were children and some parents had more than one child with them," he said. "ICE has communicated no drop offs will be taking place tomorrow, and all migrants have been received at different Annunciation House shelters."

"I believe it was around 60 (on Monday), so thankfully it was a more manageable number than the 200 the day before," Escobar told CNN.

The man Escobar is replacing in Congress, US Rep. Beto O'Rourke, D-Texas, said in a Facebook post Tuesday that another 200 people were to be released on Christmas Day and more than 500 on Wednesday.

His post included photos of migrants receiving assistance from volunteers at a shelter.

"Kids who arrived sick getting medical care, families able to have a Christmas meal together," he wrote.

In another post on Christmas Eve, O'Rourke said ICE initially "dropped the ball" by not notifying the community of the release of hundreds of migrants at the Greyhound station over the weekend.

Honduran and Guatemalan migrants were dropped off at the Rockhouse Café and Gallery in downtown El Paso to wait for buses to shelters, CNN affiliate KFOX reported Tuesday.

The migrants were serenaded by local musicians and given food and water while they waited, the station reported.

Escobar told CNN the number Wednesday could be 500, with another 500 possible on Thursday. "We never know until that very day, but that's what we're expecting," she said.

She called the numbers a "significant uptick," saying El Paso sees about 2,000 migrants a week, with the nonprofit shelter Annunciation House accepting about 200 a day. Escobar said the migrants released at the bus station Sunday and Monday were in addition to 200 people Annunciation House accepted each of those days.

O'Rourke, who is being touted as a potential Democratic presidential candidate in 2020 after losing his November bid to unseat Sen. Ted Cruz, R-Texas, spent part of Monday assisting migrants in an El Paso park near the bus station.

"We'd love to be able to get those beds ready so that folks, as you can see around us, are just sitting on the pavement and some have been here now for a couple of hours," O'Rourke said in the video. "We'd love for them to get to a shelter where there's food waiting for them, where there are beds waiting for them, and where they can call family members to let them know they're OK.

"Many of those we're seeing right now have been in detention for the last seven or eight days, they may not have had contact with family, and in some cases don't even totally know where they are in the United States."

Police in El Paso learned about the first group released around 8 p.m. Sunday when officials at the Greyhound terminal told them people were trying to board buses without tickets.

"All of a sudden a bunch of people show up; ICE drops them off," Greyhound spokeswoman Crystal Booker said. "We weren't expecting it. We (were) not given prior notice."

The waiting area at the bus terminal is small, said El Paso police spokesman Sgt. Robert Gomez, and many people were left standing outside in the cold. He said the group of undocumented immigrants included some families and small children.

Later, four buses arrived for people to board and stay warm, he said.

"We weren't going to put 200 people on the streets of El Paso on a cold night. We wouldn't do that," Gomez said.

Authorities found housing for the migrants, including at a hotel and a nearby Catholic school, he said.

"We're a little perplexed because this is not something typically that ICE does," Dylan Corbett, director of Hope Border Institute, told CNN affiliate KFOX. Corbett said ICE usually gives notice Annunciation House so it can be ready for a large number of arrivals.

ICE said in an emailed statement to CNN that after decades of inaction by Congress, the government is limited in what it can do to remove families who are in the United States illegally.

"To mitigate the risk of holding family units past the timeframe allotted to the government, ICE has curtailed reviews of post-release plans from families apprehended along the southwest border," the statement said. It did not specifically refer to the events in El Paso.

"ICE continues to work with local and state officials and (nongovernmental) partners in the area so they are prepared to provide assistance with transportation or other services."

This is the second time ICE just drops off these vulnerable families, who would've been homeless without the help of a handful of people. My statement here—and how you can help. pic.twitter.com/FVtHTSrLkJ

"The lack of community coordination by ICE, which first occurred in October, and again last night and today, demonstrates a reckless disregard for very vulnerable people, including children. It is unacceptable," she said.

"Federal law enforcement officials in El Paso have long worked closely with Annunciation House, an El Paso nonprofit that offers hospitality to immigrants. This collaboration ensures that migrants who have been processed by ICE do not end up on the streets of El Paso, homeless, hungry and without support.

"The federal government has an obligation to provide humane, temporary holding facilities for these migrants in their custody until they can be accepted by NGOs like Annunciation House. Quickly ridding themselves of those in their custody is not a solution. In fact, it puts adults and children at grave risk, and creates a crisis in our community."